Rydberg states in Hund’s case

Watson (1999) analyzes two subcases of case (d), which he calls (o+,d) and (b+ d). The good quantum numbers in the former are A+5+S+ J+Q+ls(J — sr)J (2S+ + 1 values of ft+) and in the latter subcase A +S+N+J+ls(J — sr)J (2S+ + 1 values of N+). Consider an example in which the ion-core has 1A symmetry, then the nonzero quantum numbers in both (a+,d) and (b+. d) sets of basis functions are reduced to A+N+lsNJ, which is the set of quantum numbers traditionally used to describe a Hund s case (d) Rydberg state. The larger set of quantum numbers, expressed in the form specified by Watson (1999) rather than the more familiar quantum numbers used here, is needed to uniquely specify the transformations between (core, Rydberg) composite cases when S+ 0. 

No Rydberg state ever exactly corresponds to a pure Hund s case, except at n = 00 or 3, but rather to a situation in an intermediate Hund s case, and it is necessary to choose, to describe it, a basis set corresponding to any one of the pure Hund s cases. The energy terms to be added in each Hund s case are different depending on this choice of basis set. To clarify these choices, consider first the simple case of atoms. 

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